Dislocation-free zone model of fracture

Abstract

Recent observations by electron microscopy have shown that a dislocation-free zone (DFZ) is present between the crack tip and the linear pileup of dislocations in the plastic zone. A singular integral equation is formulated to describe the equilibrium configuration of the dislocations. The distribution function of the dislocations is obtained in terms of elliptic integrals. The condition of compatibility and the elastic stress intensity factor at the crack tip are also derived. At the crack tip the stress varies as 1/√r. It is found that the stress intensity factor K is approximately a function of the length of the DFZ, whereas the externally applied stress approximately determines the length of the plastic zone. Based on the mechanism of dislocation generation at the crack tip proposed by Rice and Thomson, it is shown that the formation of the DFZ is anticipated when the stress intensity factor K is less than a critical stress intensity factor Kg defined for a spontaneous generation of dislocations. The magnitude of Kg relative to the critical stress intensity factor for brittle fracture Kc determines the brittle-ductile nature of a material.